Get agitated time after time in A&E (6)
I believe the answer is:
aerate
'get agitated' is the definition.
(to aerate is to mix or agitate with air)
'time after time in ae' is the wordplay.
'time' becomes 'era' (era is a kind of time).
'after' means one lot of letters go next to another.
'time' becomes 't' (abbreviation).
'in' indicates putting letters inside.
'era'+'t'='erat'
'erat' placed within 'ae' is 'AERATE'.
(Other definitions for aerate that I've seen before include "Charge with carbon dioxide" , "Oxygenate" , "Add fizz" , "Pass gas through" , "Fill with carbon dioxide" .)